Q107 / 200 · Manipal (MET) 2010 · Mathematics

The equation $3 x^2+7 x y+2 y^2+5 x+5 y+2=0$ represents

  • Correct answer
    A
    a pair of straight lines
  • B
    a circle
  • C
    an ellipse
  • D
    a hyperbola

Solution

The given equation is of the form $a x^2+2 k+2+2 g x+2 f y+c=0, \quad$ on comparing the given equation with it We obtain $a=3, h=\frac{7}{2}, b=2, g=\frac{5}{2}, f=\frac{5}{2}$ and $c=2$ $\begin{aligned} & \text { Now, } a b c+2 f g h-a f^2-b g^2-c h^2 \\ & =12+2 \times \frac{5}{2} \times \frac{5}{2} \times \frac{7}{2}-3\left(\frac{5}{2}\right)^2-2\left(\frac{5}{2}\right)^2-2\left(\frac{7}{2}\right)^2\end{aligned}$ $=0$

Hence, the correct answer is option: 'A'.

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